Subgroups — C₂×C₅×#5615 #14481079

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5615	C₂	1	16	yes	maximal, direct product factor
11	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#540	—	3	1	no	maximal, Hall
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
25	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
26	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
27	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
28	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
31	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	C₂²	1	8	yes	complemented
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×#217	C₂²	1	1	yes	characteristic
38	C₂×C₅×#217	C₂²	1	1	yes	characteristic
39	C₂×C₅×#217	C₂²	1	1	yes	characteristic
40	C₂×C₅×#217	C₂²	1	1	yes	characteristic
41	C₅×#940	C₂²	1	8	yes	complemented
42	C₅×#939	C₂²	1	8	yes	complemented
43	C₅×#939	C₂²	1	8	yes	complemented
44	C₅×#939	C₂²	1	8	yes	complemented
45	C₅×#938	C₂²	1	8	yes	complemented
46	C₅×#935	C₂²	1	8	yes	complemented
47	C₅×#929	C₂²	1	8	yes	complemented
48	C₄×C₅×#67	C₂²	1	8	yes	complemented
49	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
54	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
59	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
60	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
62	C₅×#894	C₂²	1	8	yes	complemented
63	C₅×#889	C₂²	1	8	yes	complemented
64	C₅×#884	C₂²	1	8	yes	complemented
65	C₅×#883	C₂²	1	8	yes	complemented
66	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
67	C₅×#877	C₂²	1	8	yes	complemented
68	C₂×#5615	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#540	—	3	16	no	—
70	C₂×C₅×#127	—	3	1	no	—
71	C₂×C₅×#125	—	3	1	no	—
72	C₂×C₅×#123	—	3	1	no	—
73	C₂×C₅×#123	—	3	1	no	—
74	C₂×C₅×#123	—	3	1	no	—
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×#121	—	3	1	no	—
77	C₂×C₅×#121	—	3	1	no	—
78	C₂×C₅×#121	—	3	1	no	—
79	C₂×C₅×#121	—	3	1	no	—
80	C₂×C₅×#121	—	3	1	no	—
81	C₂×C₅×#121	D₃	1	1	yes	characteristic, complemented
82	C₂×C₄×C₅×D₄	—	3	1	no	—
83	C₂×C₄×C₅×D₄	—	3	1	no	—
84	C₂×C₅×#117	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
87	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×D₄	—	4	2	no	—
91	C₂×C₃×C₅×D₄	—	4	2	no	—
92	C₂×C₃×C₅×D₄	—	4	2	no	—
93	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
94	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
95	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
96	C₂²×C₃×C₄×C₅	—	4	2	no	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
102	C₂×C₅×#67	—	2	4	no	—
103	C₂×C₅×#67	—	2	4	no	—
104	C₂×C₅×#67	—	4	2	no	—
105	C₂×C₅×#67	—	4	2	no	—
106	C₂×C₅×#67	—	4	2	no	—
107	C₂×C₅×#67	—	4	2	no	—
108	C₂×C₅×#67	C₂³	1	4	yes	—
109	C₂×C₅×#67	C₂³	1	4	yes	—
110	C₂×C₅×#67	C₂³	1	4	yes	—
111	C₂×C₅×#67	C₂³	1	4	yes	—
112	C₂×C₅×#67	C₂³	1	4	yes	—
113	C₂×C₅×#67	C₂³	1	4	yes	—
114	C₂²×C₅×Dic₃	—	2	4	no	—
115	C₂²×C₅×Dic₃	—	4	2	no	—
116	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
117	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
118	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
121	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
122	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
123	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
124	C₂×C₅×D₁₂	—	4	2	no	—
125	C₂×C₅×D₁₂	C₂³	1	4	yes	—
126	C₂×C₄×C₅×D₃	—	4	2	no	—
127	C₂×C₄×C₅×D₃	—	4	2	no	—
128	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
129	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
131	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
132	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
133	C₅×#217	C₂³	1	4	yes	—
134	C₅×#217	C₂³	1	4	yes	—
135	C₅×#217	C₂³	1	4	yes	—
136	C₅×#217	C₂³	1	4	yes	—
137	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
139	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
140	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
141	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
142	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
146	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
147	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
148	C₄×C₅×Dic₃	C₂³	1	4	yes	—
149	C₄×C₅×Dic₃	C₂³	1	4	yes	—
150	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×#940	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#938	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#935	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#929	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
159	#5615	C₂×C₅	1	16	yes	direct product factor
160	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂×#883	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
165	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
166	C₂²×C₅×D₄	—	3	1	no	—
167	C₂²×C₅×D₄	—	3	1	no	—
168	C₂²×C₅×D₄	—	3	1	no	—
169	C₂²×C₅×D₄	—	3	1	no	—
170	C₂²×C₅×D₄	—	3	1	no	—
171	C₂²×C₅×D₄	—	3	1	no	—
172	C₂²×C₅×D₄	—	3	1	no	—
173	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
174	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
175	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
176	C₂³×C₄×C₅	—	3	1	no	—
177	C₂³×C₄×C₅	—	3	1	no	—
178	C₂³×C₄×C₅	—	3	1	no	—
179	C₂³×C₄×C₅	—	3	1	no	—
180	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
181	C₅×#127	—	3	8	no	—
182	C₅×#125	—	3	8	no	—
183	C₅×#123	—	3	8	no	—
184	C₅×#123	—	3	8	no	—
185	C₅×#123	—	3	8	no	—
186	C₅×#123	—	3	8	no	—
187	C₅×#121	—	3	8	no	—
188	C₅×#121	—	3	8	no	—
189	C₅×#121	—	3	8	no	—
190	C₅×#121	—	3	8	no	—
191	C₅×#121	—	3	8	no	—
192	C₅×#121	C₂×D₃	1	8	yes	complemented
193	C₄×C₅×D₄	—	3	8	no	—
194	C₄×C₅×D₄	—	3	8	no	—
195	C₅×#117	—	3	8	no	—
196	C₂×C₅×C₄⋊C₄	—	3	1	no	—
197	C₂×C₅×C₄⋊C₄	—	3	1	no	—
198	C₂×C₅×C₄⋊C₄	—	3	1	no	—
199	C₂×C₅×C₄⋊C₄	—	3	1	no	—
200	C₂×C₅×C₄⋊C₄	—	3	1	no	—
201	C₂×C₅×C₄⋊C₄	—	3	1	no	—
202	C₂×C₅×C₄⋊C₄	—	3	1	no	—
203	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
204	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
205	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
206	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
207	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
208	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
209	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
210	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
211	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
212	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
213	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
214	C₂×C₄²×C₅	—	3	1	no	—
215	C₂×C₄²×C₅	—	3	1	no	—
216	C₂×#540	—	3	1	no	Sylow
217	C₂³×C₃×C₅	—	2	2	no	—
218	C₂³×C₃×C₅	—	2	2	no	—
219	C₂³×C₃×C₅	—	2	2	no	—
220	C₂³×C₃×C₅	—	2	2	no	—
221	C₂³×C₃×C₅	—	2	2	no	—
222	C₂³×C₃×C₅	—	2	2	no	—
223	C₂³×C₃×C₅	—	2	2	no	—
224	C₂³×C₃×C₅	—	2	2	no	—
225	C₂³×C₃×C₅	—	2	2	no	—
226	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
227	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
228	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
229	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
230	C₂²×C₅×D₃	—	2	2	no	—
231	C₂²×C₅×D₃	—	2	2	no	—
232	C₂²×C₅×D₃	—	2	2	no	—
233	C₂²×C₅×D₃	—	2	2	no	—
234	C₂²×C₅×D₃	—	2	2	no	—
235	C₂²×C₅×D₃	—	2	2	no	—
236	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
237	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
238	C₃×C₅×D₄	—	4	4	no	—
239	C₃×C₅×D₄	—	4	4	no	—
240	C₃×C₅×D₄	—	4	4	no	—
241	C₂×C₃×C₄×C₅	—	2	2	no	—
242	C₂×C₃×C₄×C₅	—	2	2	no	—
243	C₂×C₃×C₄×C₅	—	2	2	no	—
244	C₂×C₃×C₄×C₅	—	2	2	no	—
245	C₂×C₃×C₄×C₅	—	4	4	no	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
247	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
248	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
249	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
250	C₅×#67	—	2	8	no	—
251	C₅×#67	—	2	8	no	—
252	C₅×#67	—	4	4	no	—
253	C₅×#67	—	4	4	no	—
254	C₅×#67	—	4	4	no	—
255	C₅×#67	—	4	4	no	—
256	C₂×C₅×Dic₃	—	2	2	no	—
257	C₂×C₅×Dic₃	—	2	2	no	—
258	C₂×C₅×Dic₃	—	2	2	no	—
259	C₂×C₅×Dic₃	—	2	2	no	—
260	C₂×C₅×Dic₃	—	2	2	no	—
261	C₂×C₅×Dic₃	—	2	8	no	—
262	C₂×C₅×Dic₃	—	4	4	no	—
263	C₂×C₅×Dic₃	#41	1	4	yes	—
264	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
265	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
266	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
267	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
268	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
269	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
270	C₅×D₁₂	—	4	4	no	—
271	C₄×C₅×D₃	—	4	4	no	—
272	C₄×C₅×D₃	—	4	4	no	—
273	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
274	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
276	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
277	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
278	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
279	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
280	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
281	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
282	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
283	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
284	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
285	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
286	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
287	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
288	C₃×#121	C₂²×C₅	1	8	yes	complemented
289	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×#217	C₂²×C₅	1	1	yes	characteristic
293	C₂×#217	C₂²×C₅	1	1	yes	characteristic
294	C₂×#217	C₂²×C₅	1	1	yes	characteristic
295	C₂×#217	C₂²×C₅	1	1	yes	characteristic
296	#940	C₂²×C₅	1	8	yes	complemented
297	#939	C₂²×C₅	1	8	yes	complemented
298	#939	C₂²×C₅	1	8	yes	complemented
299	#939	C₂²×C₅	1	8	yes	complemented
300	#938	C₂²×C₅	1	8	yes	complemented
301	#935	C₂²×C₅	1	8	yes	complemented
302	#929	C₂²×C₅	1	8	yes	complemented
303	C₄×#67	C₂²×C₅	1	8	yes	complemented
304	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
305	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
306	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
307	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
309	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
310	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
311	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
312	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
313	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
314	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
315	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
316	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
317	#894	C₂²×C₅	1	8	yes	complemented
318	#889	C₂²×C₅	1	8	yes	complemented
319	#884	C₂²×C₅	1	8	yes	complemented
320	#883	C₂²×C₅	1	8	yes	complemented
321	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
322	#877	C₂²×C₅	1	8	yes	complemented
323	C₂⁴×C₅	—	3	1	no	—
324	C₂⁴×C₅	—	3	1	no	—
325	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
326	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
327	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
328	C₂×C₅×D₄	—	3	4	no	—
329	C₂×C₅×D₄	—	3	4	no	—
330	C₂×C₅×D₄	—	3	4	no	—
331	C₂×C₅×D₄	—	3	4	no	—
332	C₂×C₅×D₄	—	3	4	no	—
333	C₂×C₅×D₄	—	3	4	no	—
334	C₂×C₅×D₄	—	3	4	no	—
335	C₂×C₅×D₄	—	4	2	no	—
336	C₂×C₅×D₄	—	4	2	no	—
337	C₂×C₅×D₄	—	4	2	no	—
338	C₂×C₅×D₄	—	6	4	no	—
339	C₂×C₅×D₄	—	6	4	no	—
340	C₂×C₅×D₄	—	12	2	no	—
341	C₂×C₅×D₄	—	12	2	no	—
342	C₂×C₅×D₄	—	12	2	no	—
343	C₂×C₅×D₄	—	12	2	no	—
344	C₂×C₅×D₄	—	12	2	no	—
345	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
346	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
347	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
348	C₂²×C₄×C₅	—	3	1	no	—
349	C₂²×C₄×C₅	—	3	4	no	—
350	C₂²×C₄×C₅	—	3	1	no	—
351	C₂²×C₄×C₅	—	3	1	no	—
352	C₂²×C₄×C₅	—	3	1	no	—
353	C₂²×C₄×C₅	—	3	1	no	—
354	C₂²×C₄×C₅	—	3	1	no	—
355	C₂²×C₄×C₅	—	3	4	no	—
356	C₂²×C₄×C₅	—	3	4	no	—
357	C₂²×C₄×C₅	—	3	4	no	—
358	C₂²×C₄×C₅	—	4	2	no	—
359	C₂²×C₄×C₅	—	6	4	no	—
360	C₂²×C₄×C₅	—	12	2	no	—
361	C₂²×C₄×C₅	—	12	2	no	—
362	C₂²×C₄×C₅	—	12	2	no	—
363	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
364	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
367	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
368	C₅×C₄⋊C₄	—	3	4	no	—
369	C₅×C₄⋊C₄	—	3	4	no	—
370	C₅×C₄⋊C₄	—	3	4	no	—
371	C₅×C₄⋊C₄	—	3	4	no	—
372	C₅×C₄⋊C₄	—	3	4	no	—
373	C₅×C₄⋊C₄	—	3	4	no	—
374	C₅×C₄⋊C₄	—	3	4	no	—
375	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
376	C₅×C₂²⋊C₄	—	3	4	no	—
377	C₅×C₂²⋊C₄	—	3	4	no	—
378	C₅×C₂²⋊C₄	—	3	4	no	—
379	C₅×C₂²⋊C₄	—	3	4	no	—
380	C₅×C₂²⋊C₄	—	3	4	no	—
381	C₅×C₂²⋊C₄	—	3	4	no	—
382	C₅×C₂²⋊C₄	—	3	4	no	—
383	C₅×C₂²⋊C₄	—	3	4	no	—
384	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
385	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
386	C₄²×C₅	—	3	4	no	—
387	C₄²×C₅	—	3	4	no	—
388	#540	—	3	16	no	—
389	C₂×#127	—	3	1	no	—
390	C₂×#125	—	3	1	no	—
391	C₂×#123	—	3	1	no	—
392	C₂×#123	—	3	1	no	—
393	C₂×#123	—	3	1	no	—
394	C₂×#123	—	3	1	no	—
395	C₂×#121	—	3	1	no	—
396	C₂×#121	—	3	1	no	—
397	C₂×#121	—	3	1	no	—
398	C₂×#121	—	3	1	no	—
399	C₂×#121	—	3	1	no	—
400	C₂×#121	C₅×D₃	1	1	yes	characteristic, complemented
401	C₂×C₄×D₄	—	3	1	no	—
402	C₂×C₄×D₄	—	3	1	no	—
403	C₂×#117	—	3	1	no	—
404	C₂²×C₃×C₅	—	2	2	no	—
405	C₂²×C₃×C₅	—	2	2	no	—
406	C₂²×C₃×C₅	—	2	2	no	—
407	C₂²×C₃×C₅	—	2	2	no	—
408	C₂²×C₃×C₅	—	2	2	no	—
409	C₂²×C₃×C₅	—	2	2	no	—
410	C₂²×C₃×C₅	—	2	2	no	—
411	C₂²×C₃×C₅	—	2	2	no	—
412	C₂²×C₃×C₅	—	2	2	no	—
413	C₂²×C₃×C₅	—	4	4	no	—
414	C₂²×C₃×C₅	—	4	4	no	—
415	C₂²×C₃×C₅	—	4	4	no	—
416	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
417	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
418	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
419	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
420	C₂×C₅×D₃	—	2	2	no	—
421	C₂×C₅×D₃	—	2	2	no	—
422	C₂×C₅×D₃	—	2	2	no	—
423	C₂×C₅×D₃	—	2	2	no	—
424	C₂×C₅×D₃	—	2	2	no	—
425	C₂×C₅×D₃	—	2	2	no	—
426	C₂×C₅×D₃	—	4	4	no	—
427	C₂×C₅×D₃	—	4	4	no	—
428	C₃×C₄×C₅	—	2	2	no	—
429	C₃×C₄×C₅	—	2	2	no	—
430	C₃×C₄×C₅	—	2	2	no	—
431	C₃×C₄×C₅	—	2	2	no	—
432	C₅×Dic₃	—	2	2	no	—
433	C₅×Dic₃	—	2	2	no	—
434	C₅×Dic₃	—	2	2	no	—
435	C₅×Dic₃	—	2	2	no	—
436	C₅×Dic₃	—	2	2	no	—
437	C₅×Dic₃	C₂×#41	1	4	yes	—
438	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
439	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
440	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
441	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
442	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₃×D₄	—	4	2	no	—
444	C₂×C₃×D₄	—	4	2	no	—
445	C₂×C₃×D₄	—	4	2	no	—
446	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
447	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
448	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
449	C₂²×C₃×C₄	—	4	2	no	—
450	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
451	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
452	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
453	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
455	C₂×#67	—	2	4	no	—
456	C₂×#67	—	2	4	no	—
457	C₂×#67	—	4	2	no	—
458	C₂×#67	—	4	2	no	—
459	C₂×#67	—	4	2	no	—
460	C₂×#67	—	4	2	no	—
461	C₂×#67	C₂³×C₅	1	4	yes	—
462	C₂×#67	C₂³×C₅	1	4	yes	—
463	C₂×#67	C₂³×C₅	1	4	yes	—
464	C₂×#67	C₂³×C₅	1	4	yes	—
465	C₂×#67	C₂³×C₅	1	4	yes	—
466	C₂×#67	C₂³×C₅	1	4	yes	—
467	C₂²×Dic₃	—	2	4	no	—
468	C₂²×Dic₃	—	4	2	no	—
469	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
470	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
471	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
472	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
473	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
474	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
475	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
476	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
477	C₂×D₁₂	—	4	2	no	—
478	C₂×D₁₂	C₂³×C₅	1	4	yes	—
479	C₂×C₄×D₃	—	4	2	no	—
480	C₂×C₄×D₃	—	4	2	no	—
481	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
482	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
483	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
484	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
485	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
486	#217	C₂³×C₅	1	4	yes	—
487	#217	C₂³×C₅	1	4	yes	—
488	#217	C₂³×C₅	1	4	yes	—
489	#217	C₂³×C₅	1	4	yes	—
490	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
491	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
492	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
493	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
494	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
495	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
496	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
497	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
498	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
499	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
500	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
501	C₄×Dic₃	C₂³×C₅	1	4	yes	—
502	C₄×Dic₃	C₂³×C₅	1	4	yes	—
503	C₂³×C₅	—	2	2	no	—
504	C₂³×C₅	—	2	2	no	—
505	C₂³×C₅	—	2	2	no	—
506	C₂³×C₅	—	2	2	no	—
507	C₂³×C₅	—	2	2	no	—
508	C₂³×C₅	—	2	2	no	—
509	C₂³×C₅	—	2	2	no	—
510	C₂³×C₅	—	2	2	no	—
511	C₂³×C₅	—	2	2	no	—
512	C₂³×C₅	—	3	2	no	—
513	C₂³×C₅	—	3	2	no	—
514	C₂³×C₅	—	6	2	no	—
515	C₂³×C₅	—	6	2	no	—
516	C₂³×C₅	—	6	2	no	—
517	C₂³×C₅	—	6	2	no	—
518	C₂³×C₅	—	6	2	no	—
519	C₂³×C₅	—	6	2	no	—
520	C₂³×C₅	C₂³×D₃	1	2	yes	—
521	C₂³×C₅	C₂³×D₃	1	2	yes	—
522	C₂³×C₅	C₂³×D₃	1	2	yes	—
523	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
524	C₅×D₄	—	4	4	no	—
525	C₅×D₄	—	4	4	no	—
526	C₅×D₄	—	4	4	no	—
527	C₅×D₄	—	6	8	no	—
528	C₅×D₄	—	6	8	no	—
529	C₅×D₄	—	12	4	no	—
530	C₅×D₄	—	12	4	no	—
531	C₅×D₄	—	12	4	no	—
532	C₅×D₄	—	12	4	no	—
533	C₅×D₄	—	12	4	no	—
534	C₂×C₄×C₅	—	2	2	no	—
535	C₂×C₄×C₅	—	2	2	no	—
536	C₂×C₄×C₅	—	2	2	no	—
537	C₂×C₄×C₅	—	2	2	no	—
538	C₂×C₄×C₅	—	3	4	no	—
539	C₂×C₄×C₅	—	3	2	no	—
540	C₂×C₄×C₅	—	3	2	no	—
541	C₂×C₄×C₅	—	3	2	no	—
542	C₂×C₄×C₅	—	3	2	no	—
543	C₂×C₄×C₅	—	3	2	no	—
544	C₂×C₄×C₅	—	3	2	no	—
545	C₂×C₄×C₅	—	4	4	no	—
546	C₂×C₄×C₅	—	6	8	no	—
547	C₂×C₄×C₅	—	6	2	no	—
548	C₂×C₄×C₅	—	6	2	no	—
549	C₂×C₄×C₅	—	6	2	no	—
550	C₂×C₄×C₅	—	6	2	no	—
551	C₂×C₄×C₅	—	6	2	no	—
552	C₂×C₄×C₅	—	12	4	no	—
553	C₂×C₄×C₅	—	12	4	no	—
554	C₂×C₄×C₅	—	12	4	no	—
555	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
556	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
557	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
558	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
559	C₂²×D₄	—	3	1	no	—
560	C₂²×D₄	—	3	1	no	—
561	C₂²×D₄	—	3	1	no	—
562	C₂²×D₄	—	3	1	no	—
563	C₂²×D₄	—	3	1	no	—
564	C₂²×D₄	—	3	1	no	—
565	C₂²×D₄	—	3	1	no	—
566	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
567	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
568	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
569	C₂³×C₄	—	3	1	no	—
570	C₂³×C₄	—	3	1	no	—
571	C₂³×C₄	—	3	1	no	—
572	C₂³×C₄	—	3	1	no	—
573	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
574	#127	—	3	8	no	—
575	#125	—	3	8	no	—
576	#123	—	3	8	no	—
577	#123	—	3	8	no	—
578	#123	—	3	8	no	—
579	#123	—	3	8	no	—
580	#121	—	3	8	no	—
581	#121	—	3	8	no	—
582	#121	—	3	8	no	—
583	#121	—	3	8	no	—
584	#121	—	3	8	no	—
585	#121	C₂×C₅×D₃	1	8	yes	complemented
586	C₄×D₄	—	3	8	no	—
587	C₄×D₄	—	3	8	no	—
588	#117	—	3	8	no	—
589	C₂×C₄⋊C₄	—	3	1	no	—
590	C₂×C₄⋊C₄	—	3	1	no	—
591	C₂×C₄⋊C₄	—	3	1	no	—
592	C₂×C₄⋊C₄	—	3	1	no	—
593	C₂×C₄⋊C₄	—	3	1	no	—
594	C₂×C₄⋊C₄	—	3	1	no	—
595	C₂×C₄⋊C₄	—	3	1	no	—
596	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	—	3	1	no	—
598	C₂×C₂²⋊C₄	—	3	1	no	—
599	C₂×C₂²⋊C₄	—	3	1	no	—
600	C₂×C₂²⋊C₄	—	3	1	no	—
601	C₂×C₂²⋊C₄	—	3	1	no	—
602	C₂×C₂²⋊C₄	—	3	1	no	—
603	C₂×C₂²⋊C₄	—	3	1	no	—
604	C₂×C₂²⋊C₄	—	3	1	no	—
605	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
606	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
607	C₂×C₄²	—	3	1	no	—
608	C₂×C₄²	—	3	1	no	—
609	C₂×C₃×C₅	—	4	2	no	—
610	C₂×C₃×C₅	—	4	2	no	—
611	C₂×C₃×C₅	—	4	2	no	—
612	C₂×C₃×C₅	#540	1	4	yes	complemented
613	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
614	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₅×D₃	—	4	2	no	—
617	C₅×D₃	—	4	2	no	—
618	C₂³×C₃	—	2	2	no	—
619	C₂³×C₃	—	2	2	no	—
620	C₂³×C₃	—	2	2	no	—
621	C₂³×C₃	—	2	2	no	—
622	C₂³×C₃	—	2	2	no	—
623	C₂³×C₃	—	2	2	no	—
624	C₂³×C₃	—	2	2	no	—
625	C₂³×C₃	—	2	2	no	—
626	C₂³×C₃	—	2	2	no	—
627	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
628	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
629	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
630	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
631	C₂²×D₃	—	2	2	no	—
632	C₂²×D₃	—	2	2	no	—
633	C₂²×D₃	—	2	2	no	—
634	C₂²×D₃	—	2	2	no	—
635	C₂²×D₃	—	2	2	no	—
636	C₂²×D₃	—	2	2	no	—
637	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
638	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
639	C₃×D₄	—	4	4	no	—
640	C₃×D₄	—	4	4	no	—
641	C₃×D₄	—	4	4	no	—
642	C₂×C₃×C₄	—	2	2	no	—
643	C₂×C₃×C₄	—	2	2	no	—
644	C₂×C₃×C₄	—	2	2	no	—
645	C₂×C₃×C₄	—	2	2	no	—
646	C₂×C₃×C₄	—	4	4	no	—
647	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
648	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
649	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
650	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
651	#67	—	2	8	no	—
652	#67	—	2	8	no	—
653	#67	—	4	4	no	—
654	#67	—	4	4	no	—
655	#67	—	4	4	no	—
656	#67	—	4	4	no	—
657	C₂×Dic₃	—	2	2	no	—
658	C₂×Dic₃	—	2	2	no	—
659	C₂×Dic₃	—	2	2	no	—
660	C₂×Dic₃	—	2	2	no	—
661	C₂×Dic₃	—	2	2	no	—
662	C₂×Dic₃	—	2	8	no	—
663	C₂×Dic₃	—	4	4	no	—
664	C₂×Dic₃	C₅×#41	1	4	yes	—
665	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
666	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
667	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
668	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
669	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
670	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
671	D₁₂	—	4	4	no	—
672	C₄×D₃	—	4	4	no	—
673	C₄×D₃	—	4	4	no	—
674	C₂²×C₅	—	2	2	no	—
675	C₂²×C₅	—	2	2	no	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	2	no	—
683	C₂²×C₅	—	4	4	no	—
684	C₂²×C₅	—	4	4	no	—
685	C₂²×C₅	—	4	4	no	—
686	C₂²×C₅	—	6	2	no	—
687	C₂²×C₅	—	6	2	no	—
688	C₂²×C₅	—	6	2	no	—
689	C₂²×C₅	—	6	2	no	—
690	C₂²×C₅	—	6	2	no	—
691	C₂²×C₅	—	6	2	no	—
692	C₂²×C₅	—	12	4	no	—
693	C₂²×C₅	—	12	4	no	—
694	C₂²×C₅	#1004	1	2	yes	—
695	C₂²×C₅	#1004	1	2	yes	—
696	C₂²×C₅	D₃×#41	1	2	yes	—
697	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
698	C₄×C₅	—	2	2	no	—
699	C₄×C₅	—	2	2	no	—
700	C₄×C₅	—	2	2	no	—
701	C₄×C₅	—	2	2	no	—
702	C₄×C₅	—	3	4	no	—
703	C₄×C₅	—	6	2	no	—
704	C₄×C₅	—	6	2	no	—
705	C₄×C₅	—	6	2	no	—
706	C₄×C₅	—	6	2	no	—
707	C₄×C₅	—	6	2	no	—
708	C₂⁴	—	3	1	no	—
709	C₂⁴	—	3	1	no	—
710	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
711	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
713	C₂×D₄	—	3	4	no	—
714	C₂×D₄	—	3	4	no	—
715	C₂×D₄	—	3	4	no	—
716	C₂×D₄	—	3	4	no	—
717	C₂×D₄	—	3	4	no	—
718	C₂×D₄	—	3	4	no	—
719	C₂×D₄	—	3	4	no	—
720	C₂×D₄	—	4	2	no	—
721	C₂×D₄	—	4	2	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	6	4	no	—
724	C₂×D₄	—	6	4	no	—
725	C₂×D₄	—	12	2	no	—
726	C₂×D₄	—	12	2	no	—
727	C₂×D₄	—	12	2	no	—
728	C₂×D₄	—	12	2	no	—
729	C₂×D₄	—	12	2	no	—
730	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
731	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
732	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
733	C₂²×C₄	—	3	1	no	—
734	C₂²×C₄	—	3	1	no	—
735	C₂²×C₄	—	3	1	no	—
736	C₂²×C₄	—	3	1	no	—
737	C₂²×C₄	—	3	1	no	—
738	C₂²×C₄	—	3	1	no	—
739	C₂²×C₄	—	3	4	no	—
740	C₂²×C₄	—	3	4	no	—
741	C₂²×C₄	—	3	4	no	—
742	C₂²×C₄	—	3	4	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	6	4	no	—
745	C₂²×C₄	—	12	2	no	—
746	C₂²×C₄	—	12	2	no	—
747	C₂²×C₄	—	12	2	no	—
748	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
749	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
750	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
751	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
752	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
753	C₄⋊C₄	—	3	4	no	—
754	C₄⋊C₄	—	3	4	no	—
755	C₄⋊C₄	—	3	4	no	—
756	C₄⋊C₄	—	3	4	no	—
757	C₄⋊C₄	—	3	4	no	—
758	C₄⋊C₄	—	3	4	no	—
759	C₄⋊C₄	—	3	4	no	—
760	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
761	C₂²⋊C₄	—	3	4	no	—
762	C₂²⋊C₄	—	3	4	no	—
763	C₂²⋊C₄	—	3	4	no	—
764	C₂²⋊C₄	—	3	4	no	—
765	C₂²⋊C₄	—	3	4	no	—
766	C₂²⋊C₄	—	3	4	no	—
767	C₂²⋊C₄	—	3	4	no	—
768	C₂²⋊C₄	—	3	4	no	—
769	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
770	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
771	C₄²	—	3	4	no	—
772	C₄²	—	3	4	no	—
773	C₃×C₅	C₂×#540	1	1	yes	characteristic, complemented, Hall
774	C₂²×C₃	—	2	2	no	—
775	C₂²×C₃	—	2	2	no	—
776	C₂²×C₃	—	2	2	no	—
777	C₂²×C₃	—	2	2	no	—
778	C₂²×C₃	—	2	2	no	—
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	4	4	no	—
784	C₂²×C₃	—	4	4	no	—
785	C₂²×C₃	—	4	4	no	—
786	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
787	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
788	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
789	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
790	C₂×D₃	—	2	2	no	—
791	C₂×D₃	—	2	2	no	—
792	C₂×D₃	—	2	2	no	—
793	C₂×D₃	—	2	2	no	—
794	C₂×D₃	—	2	2	no	—
795	C₂×D₃	—	2	2	no	—
796	C₂×D₃	—	4	4	no	—
797	C₂×D₃	—	4	4	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	2	no	—
801	C₃×C₄	—	2	2	no	—
802	Dic₃	—	2	2	no	—
803	Dic₃	—	2	2	no	—
804	Dic₃	—	2	2	no	—
805	Dic₃	—	2	2	no	—
806	Dic₃	—	2	2	no	—
807	Dic₃	C₂×C₅×#41	1	4	yes	—
808	C₂×C₅	—	4	2	no	—
809	C₂×C₅	—	4	2	no	—
810	C₂×C₅	—	4	2	no	—
811	C₂×C₅	—	12	2	no	—
812	C₂×C₅	—	12	2	no	—
813	C₂×C₅	#5615	1	4	yes	direct product factor
814	C₂×C₅	C₂×#1004	1	1	yes	characteristic
815	C₂×C₅	C₂×#1004	1	1	yes	characteristic
816	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	3	2	no	—
827	C₂³	—	3	2	no	—
828	C₂³	—	6	2	no	—
829	C₂³	—	6	2	no	—
830	C₂³	—	6	2	no	—
831	C₂³	—	6	2	no	—
832	C₂³	—	6	2	no	—
833	C₂³	—	6	2	no	—
834	C₂³	C₂³×C₅×D₃	1	2	yes	—
835	C₂³	C₂³×C₅×D₃	1	2	yes	—
836	C₂³	C₂³×C₅×D₃	1	2	yes	—
837	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
838	D₄	—	4	4	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	4	no	—
841	D₄	—	6	8	no	—
842	D₄	—	6	8	no	—
843	D₄	—	12	4	no	—
844	D₄	—	12	4	no	—
845	D₄	—	12	4	no	—
846	D₄	—	12	4	no	—
847	D₄	—	12	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	3	4	no	—
853	C₂×C₄	—	3	2	no	—
854	C₂×C₄	—	3	2	no	—
855	C₂×C₄	—	3	2	no	—
856	C₂×C₄	—	3	2	no	—
857	C₂×C₄	—	3	2	no	—
858	C₂×C₄	—	3	2	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	6	8	no	—
861	C₂×C₄	—	6	2	no	—
862	C₂×C₄	—	6	2	no	—
863	C₂×C₄	—	6	2	no	—
864	C₂×C₄	—	6	2	no	—
865	C₂×C₄	—	6	2	no	—
866	C₂×C₄	—	12	4	no	—
867	C₂×C₄	—	12	4	no	—
868	C₂×C₄	—	12	4	no	—
869	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
870	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
871	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
872	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
873	C₂×C₃	—	4	2	no	—
874	C₂×C₃	—	4	2	no	—
875	C₂×C₃	—	4	2	no	—
876	C₂×C₃	C₅×#540	1	4	yes	complemented
877	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
878	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
879	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
880	D₃	—	4	2	no	—
881	D₃	—	4	2	no	—
882	C₅	C₂×#5615	1	1	yes	characteristic, direct product factor, Sylow
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	6	2	no	—
896	C₂²	—	6	2	no	—
897	C₂²	—	6	2	no	—
898	C₂²	—	6	2	no	—
899	C₂²	—	6	2	no	—
900	C₂²	—	6	2	no	—
901	C₂²	—	12	4	no	—
902	C₂²	—	12	4	no	—
903	C₂²	C₅×#1004	1	2	yes	—
904	C₂²	C₅×#1004	1	2	yes	—
905	C₂²	C₅×D₃×#41	1	2	yes	—
906	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
907	C₄	—	2	2	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	3	4	no	—
912	C₄	—	6	2	no	—
913	C₄	—	6	2	no	—
914	C₄	—	6	2	no	—
915	C₄	—	6	2	no	—
916	C₄	—	6	2	no	—
917	C₃	C₂×C₅×#540	1	1	yes	characteristic, complemented, Sylow
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	4	2	no	—
921	C₂	—	12	2	no	—
922	C₂	—	12	2	no	—
923	C₂	C₅×#5615	1	4	yes	direct product factor
924	C₂	C₂×C₅×#1004	1	1	yes	characteristic
925	C₂	C₂×C₅×#1004	1	1	yes	characteristic
926	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#121	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₂×C₅×#540
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₂×C₅×#940	C₂	semidirect
3. C₂×C₅×#939	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂×C₅×#939	C₂	semidirect
6. C₂×C₅×#938	C₂	semidirect
7. C₂×C₅×#935	C₂	semidirect
8. C₂×C₅×#929	C₂	semidirect
9. C₂×C₄×C₅×#67	C₂	semidirect
10. C₅×#5615	C₂	direct (N × H)
11. C₂×C₅×#894	C₂	semidirect
12. C₂×C₅×#889	C₂	semidirect
13. C₂×C₅×#884	C₂	semidirect
14. C₂×C₅×#883	C₂	semidirect
15. C₂×C₅×#67⋊C₄	C₂	semidirect
16. C₂×C₅×#877	C₂	semidirect
33. C₃×C₅×#121	C₂²	semidirect
41. C₅×#940	C₂²	semidirect
42. C₅×#939	C₂²	semidirect
43. C₅×#939	C₂²	semidirect
44. C₅×#939	C₂²	semidirect
45. C₅×#938	C₂²	semidirect
46. C₅×#935	C₂²	semidirect
47. C₅×#929	C₂²	semidirect
48. C₄×C₅×#67	C₂²	semidirect
62. C₅×#894	C₂²	semidirect
63. C₅×#889	C₂²	semidirect
64. C₅×#884	C₂²	semidirect
65. C₅×#883	C₂²	semidirect
66. C₅×#67⋊C₄	C₂²	semidirect
67. C₅×#877	C₂²	semidirect
68. C₂×#5615	C₅	direct (N × H)
81. C₂×C₅×#121	D₃	semidirect
150. C₂×C₃×#121	C₂×C₅	semidirect
151. C₂×#940	C₂×C₅	semidirect
152. C₂×#939	C₂×C₅	semidirect
153. C₂×#939	C₂×C₅	semidirect
154. C₂×#939	C₂×C₅	semidirect
155. C₂×#938	C₂×C₅	semidirect
156. C₂×#935	C₂×C₅	semidirect
157. C₂×#929	C₂×C₅	semidirect
158. C₂×C₄×#67	C₂×C₅	semidirect
159. #5615	C₂×C₅	direct (N × H)
160. C₂×#894	C₂×C₅	semidirect
161. C₂×#889	C₂×C₅	semidirect
162. C₂×#884	C₂×C₅	semidirect
163. C₂×#883	C₂×C₅	semidirect
164. C₂×#67⋊C₄	C₂×C₅	semidirect
165. C₂×#877	C₂×C₅	semidirect
192. C₅×#121	C₂×D₃	semidirect
288. C₃×#121	C₂²×C₅	semidirect
296. #940	C₂²×C₅	semidirect
297. #939	C₂²×C₅	semidirect
298. #939	C₂²×C₅	semidirect
299. #939	C₂²×C₅	semidirect
300. #938	C₂²×C₅	semidirect
301. #935	C₂²×C₅	semidirect
302. #929	C₂²×C₅	semidirect
303. C₄×#67	C₂²×C₅	semidirect
317. #894	C₂²×C₅	semidirect
318. #889	C₂²×C₅	semidirect
319. #884	C₂²×C₅	semidirect
320. #883	C₂²×C₅	semidirect
321. #67⋊C₄	C₂²×C₅	semidirect
322. #877	C₂²×C₅	semidirect
400. C₂×#121	C₅×D₃	semidirect
585. #121	C₂×C₅×D₃	semidirect
612. C₂×C₃×C₅	#540	semidirect
773. C₃×C₅	C₂×#540	semidirect
813. C₂×C₅	#5615	direct (N × H)
876. C₂×C₃	C₅×#540	semidirect
882. C₅	C₂×#5615	direct (N × H)
917. C₃	C₂×C₅×#540	semidirect
923. C₂	C₅×#5615	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#121	2
C₂×C₅×#940	2
C₂×C₅×#939	2
C₂×C₅×#938	2
C₂×C₅×#935	2
C₂×C₅×#929	2
C₂×C₄×C₅×#67	2
C₅×#5615	2
C₂×C₅×#894	2
C₂×C₅×#889	2
C₂×C₅×#884	2
C₂×C₅×#883	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#877	2
C₂×C₅×#540	3
C₂×#5615	5

Subgroups — C2×C5×#5615 #14481079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5615 #14481079